a quantitative model of slow recoveries from financial...

A Quantitative Model of Slow Recoveriesfrom

Financial Crises∗

Albert Queraltó†

Federal Reserve Board

January 2013

Abstract

Financial crises tend to be followed by slow recoveries. Evidence from emerging market economiessuggests an important role of labor productivity in accounting for the size and persistence of the out-put loss. This paper introduces a quantitative macroeconomic model consistent with these facts. Themodel features endogenous growth in total factor productivity through the adoption of new varieties ofintermediate goods, and an agency problem in financial markets which implies that technology adoptersmay be credit constrained. A crisis shock generates declines in productivity, employment and output ofsize and persistence comparable to the data. The financial friction plays a quantitatively important role,explaining between a third and a half of the medium-run drop in output. Both endogenous growth andthe financial friction substantially contribute to amplified movements in consumption and in the currentaccount. The model’s transmission mechanism is shown to be especially sensitive to financial shocks.

∗I wish to thank Mark Gertler for guidance and assistance throughout this project. I also thank Diego Comin, Jordi Galí,John Leahy, Virgiliu Midrigan, Vivian Yue and seminar participants at various venues for helpful comments. The views in thispaper are solely the responsibility of the author and should not be interpreted as reflecting the views of the Board of Governorsof the Federal Reserve System or of any other person associated with the Federal Reserve System.†Division of International Finance, Trade and Financial Studies. Email: albert.queralto@frb.gov

1 Introduction

Financial crises are frequently followed by slow recoveries. In their study of financial crises

throughout history, Reinhart and Rogoff (2009) document that these types of episodes display

the regularity that the post-crisis recovery is usually very weak. Recent research by Cerra

and Saxena (2008) has provided further evidence corroborating this fact: by analyzing the

behavior of output following episodes of financial crisis across a large set of countries, they

conclude that there is little evidence of recovery following the crisis shock. In this paper, I

first present evidence from crises in emerging market economies showing that an important

part of the output decline associated with these episodes is due to a fall in labor productivity,

which also displays considerable persistence. As shown in Section 2, productivity lost during

financial crises tends not to be regained on average – if and when productivity growth

resumes, it appears to do so from a level permanently below the pre-crisis trend.

The goal of this paper is to introduce a quantitative macroeconomic model that can ex-

plain the phenomenon of slow recoveries following financial crises. I argue that the findings

described above pose a challenge to conventional explanations for the decline in measured

labor productivity and total factor productivity (TFP) during financial crises, such as re-

duced capacity utilization or labor hoarding. While these mechanisms offer a reasonable

account for the short-run declines in measured factor productivity, it is hard to imagine why

they might persist into the medium run, once the crisis episode is over. Instead, this paper

proposes to model explicitly medium-run productivity growth through the introduction of

new technologies, and to illustrate how this process may be disrupted by a large shock and

the ensuing financial distress. At the end of section 2, some evidence is presented which

lends support to the mechanism proposed in the model, by examining the behavior of time

series data on patents and trademarks during the crisis in South Korea in 1997.

In the model, described in Section 3, TFP growth arises endogenously through the adop-

tion of new technologies. I use a formulation similar to Romer (1990), whereby endogenous

growth results from the development and adoption of new varieties of intermediate goods.

To motivate an imperfection in financial markets I use an approach similar to traditional

“financial accelerator” models. In particular, I introduce a special class of agents, called

entrepreneurs, who are assumed to be the only ones capable of introducing new varieties of

intermediates. The activity of entrepreneurs consists of borrowing funds from households

and from abroad to invest them in projects which, if successful, become usable designs for

new intermediates. The financial friction takes the form of a limited enforcement problem be-

tween entrepreneurs and lenders, whereby at any point in time the entrepreneur can renegue

on his debt and divert a certain fraction of his resources, at which point creditors can force

him into bankruptcy. The limited enforcement friction effectively introduces an endogenous

constraint on entrepreneurial debt which potentially tightens as economic conditions worsen.

The mechanism just described is embedded in an otherwise reasonably conventional small

open economy real business cycle model, modified to allow for variable capital utilization,

habit formation in consumption and a working capital requirement which forces final goods

producers to pay a fraction of the wage bill before production. These ingredients are relatively

standard in the emerging markets business cycles literature. Although not critical for the

main results regarding the lack of recovery from financial crises, which arise due to the novel

mechanism linking technology adoption to financial frictions, these features help in making

the short-run behavior of the model more realistic.

Section 4 presents a quantitative analysis of the model. The main experiment is meant

as an illustration of how a crisis such as the one that occurred in East Asia in 1997, and the

ensuing sharp deterioration in credit conditions, can generate the large and persistent decline

in productivity observed in the data. The initiating disturbance is a shock to country risk.

The interest rate increase, and the resulting drop in the values of adopted and unadopted

technologies, generates a decline in entrepreneurial wealth, which increases the severity of

the agency problem between entrepreneurs and their creditors. As a result, entrepreneurs’

constraints in their access to external finance tighten. The result at the macroeconomic level

is a substantial reduction of the pace at which the entrepreneurial sector introduces new

varieties of intermediates, leading aggregate TFP to drop permanently as a result.

The decline in TFP arising from the slowdown in the rate of technology adoption works

to reduce aggregate labor demand. As a result, employment as well remains persistently

depressed following the crisis, consistent with the empirical evidence. The magnitudes of

the declines in output, productivity and employment produced by the baseline model are

comparable to their empirical counterparts, documented in Section 2 below. The financial

friction plays a quantitatively important role in amplifying the responses of these variables

to the interest rate shock: for the baseline calibration, the degree of amplification is on

the order of fifty percent. Further, as I show in a second experiment, the model can also

be used to motivate a financial crisis through an intensification of the agency problem in

financial markets, modelled as a reduction in the parameter that governs the amount of

resources that creditors can expect to recover from a defaulting entrepreneur. Quantitative

experiments illustrate that this type of disturbance works to further deepen the magnitude

of the persistent declines in productivity, employment and output, thereby contributing to

explain the slow recovery in a quantitatively significant way.

In a final set of experiments, I analyze the behavior of the model following two types of

nonfinancial shocks: exogenous TFP shocks and wage markup shocks. The main result here

is that the transmission mechanism proposed in this paper is substantially less sensitive to

these types of disturbances than it is to financial shocks. Thus, the model is also consistent

with the evidence that prolonged slumps appear to be a phenomenon especially linked to

financial crises.

Related Literature. As mentioned above, the evidence presented in this paper on the

effects of financial crises on output, labor productivity and employment extends a recent

paper by Cerra and Saxena (2008), who document that financial crises and other large

negative shocks tend to have lasting effects on output. Using a similar methodology, I

study the response of a decomposition of output into employment and labor productivity,

finding a significant role for labor productivity in emerging economies. Other authors have

documented large TFP losses in certain episodes of financial crisis, for example Meza and

Quintin (2005), Kehoe and Ruhl (2009) or Pratap and Urrutia (2010). The results presented

in this paper are consistent with theirs, and further show that productivity losses tend to be

very persistent and are extensive to other episodes in other emerging countries.

The model developed in this paper follows Comin and Gertler (2006) in using the ex-

panding variety formulation due to Romer (1990) to endogenize medium-run productivity

dynamics. Comin and Gertler (2006) show that in the U.S. both TFP and R&D move

procyclically at medium frequencies, and present a model that can account for short and

medium term fluctuations in these and other variables. Comin, Loayza, Pasha and Serven

(2009) also use an expanding variety formulation to model the diffusion of technologies from

the U.S. to Mexico, and use their model to analyze how business fluctuations are interre-

lated in these two countries. These frameworks as well as mine share an emphasis on the

importance of modelling business cycles and productivity growth as interrelated phenomena,

a point that is reinforced by the evidence presented below showing a period of persistently

lower productivity growth following financial crises. A similar point is emphasized by Fatas

(2000a, 2000b), who documents a strong cross-country correlation between long-term growth

rates and the persistence of output fluctuations – a natural outcome in a model featuring

endogenous growth as shown in Fatas (2000a), and which is also consistent with the model

studied in this paper.

The financial imperfection introduced in this paper builds on ideas from the literature on

financial factors in macroeconomics, reviewed for example in Bernanke, Gertler and Gilchrist

(1999) or Gertler and Kiyotaki (2010). This paper follows Gertler and Kiyotaki (2010) and

others in modeling credit market imperfections through a limited enforcement problem. The

main difference with more traditional “financial accelerator” models and the present paper is

that here the credit market imperfection affects technology adoption, which is the ultimate

source of productivity growth in the model economy. Aoki, Benigno and Kiyotaki (2007,

2009) also introduce a model with credit constraints in which a crisis can endogenously

generate a drop in aggregate TFP, in their case because of productive units which are het-

erogeneus in their productivities: in their model, a crisis shock affects relatively more the

more productive agents which leverage more than the less productive agents, and aggregate

TFP declines as a result. Gopinath and Neiman (2011) present a model where the drop in

imported varieties of goods that takes place during a large crisis generates declines in TFP.

This paper differs from these other studies by emphasizing technology adoption in explaining

medium-run TFP dynamics.

Finally, this paper is related to a growing literature on quantitative business cycle frame-

works for emerging countries. Uribe and Yue (2006) and Neumeyer and Perri (2005) find an

important role for fluctuations in interest rates and country risk in accounting for emerging

market business cycles. Mendoza and Yue (2011) present a model which endogenizes fluctu-

ations in country risk, by incorporating sovereign default within a business cycle framework.

Their model also generates a drop in TFP during a crisis, due to a reduction in the use of

imported inputs by firms. The main difference with the present paper in this respect is that

here the goal is to account for the persistence of the fall in TFP following a crisis. Gertler,

Gilchrist an Natalucci (2007) present a model featuring a financial accelerator designed to

capture the Korean crisis in 1997-98, which they model as a country interest rate shock,

and use their model to illustrate how a fixed exchange rate regime can exacerbate the crisis.

Aguiar and Gopinath (2007) argue that what differentiates emerging markets from small

developed economies is a more volatile and persistent nonstationary component of TFP, a

hypothesis which the evidence presented in this paper lends support to. Further, this paper

shows that such TFP process, which is assumed exogenously in Aguiar and Gopinath (2007),

can be a natural result in a context in which TFP growth is endogenous and potentially af-

fected by imperfections in financial markets.

The rest of the paper is organized as follows. In Section 2, I present the evidence on the

effects of finacial crises. In Section 3 I describe the model. In Section 4 I present numerical

simulations of the model. Section 5 concludes.

2 Financial Crises and Productivity: Evidence

This section provides evidence on the medium-run dynamics of output following financial

crises, and examines the extent to which they are driven by movements in employment and

in labor productivity. I begin by showing that the Asian crisis in 1997 resulted in permanent

output losses for the countries involved, largely driven by a permanent decline in labor

productivity. I then go on to show, using more formal VAR methods, that this phenomenon is

quite general across episodes of banking crises in emerging economies. Finally, I present some

evidence on patents and trademarks, two indicators of technology innovation and adoption,1

during the Korean 1997 crisis. The evidence shows large declines in both indicators during

the crisis, which also featured a very persistent decline in TFP relative to trend.

Figure 1 plots output, employment and labor productivity for a group of Asian countries

around the crisis episode of 1997. The countries included are Indonesia, Malaysia, Phillip-

ines, Korea, Thailand and Hong Kong, labelled “SEA-6”. I compute area totals by adding

constant dollar, PPP-adjusted GDP for each of the countries. Labor productivity is defined

as output per employed worker. All data are from the Total Economy Database.

The first panel of Figure 1 illustrates a very persistent output loss following the crisis:

trend output is not regained, but rather output growth appears to resume from a level per-

manently below the pre-crisis trend.2 Looking at the second and third panels, the behavior

of output appears to be driven largely by labor productivity, with a more modest slowdown

of employment growth.

Figure 2 examines more closely the behavior of labor productivity. The picture suggests

that productivity did not recover to its pre-crisis trend. As the second panel shows, it falls

by about 10% relative to trend and it never rebounds. This is robust to different choices for

the pre-crisis period3.

Next I extend the evidence in Cerra and Saxena (2008), who analyze the response of

output to financial crises, to investigate the roles of employment and labor productivity in

accounting for the output loss. I use a decomposition of real output (Yt) into employment

(Lt) and labor productivity as follows:

log(Yt) = log(YtLt

) + log(Lt) = ylt + lt

where ylt ≡ log( YtLt

) and lt ≡ log(Lt). Following Cerra and Saxena (2008), I estimate the

following panel VAR:

xi,t = ai +4∑j=1

Ajxi,t−j +4∑s=0

BsDi,t−s + εi,t (1)

1See Griliches (1990) and Jaffe and Trajtenberg (2002) for discussions on patents as indicators of tech-nological change, and Yorukolgu (2000) for an example of work using trademarks data.

2the pre-crisis trend is calculated as a linear trend for the period 1980-1996.3The annualized growth of labor productivity for the period 1980-1996 is 4.06%, which is close to that for

the entire pre-crisis sample (1960-1996), equal to 3.69%. Annualized productivity growth for the post-crisisperiod of 1998-2007 is 3.61%.

xi,t =

[∆yli,t

∆ni,t

]Di,t is a dummy variable indicating a banking crisis during year t in country i, and ai is

a country fixed effect. I estimate equation (1) using banking crisis indicators, on data for a

group of emerging economies.4 I use the same crisis indicators as Cerra and Saxena (2008),

who obtain banking crisis indicators from Caprio and Klingebiel (2003): a banking crisis is

an episode in which a large fraction of bank capital is exhausted. Yearly data on real output

and employment for the period 1950-2005 is from the Total Economy database.

Figure 3 contains impulse responses of output, labor productivity and employment, to-

gether with one-standard-error bands. The first row echoes the results in Cerra and Saxena

(2008): banking crises episodes involve large and persistent losses in output, which falls by

about 8% as a result of the crisis, with little evidence of recovery. The decomposition of

output into labor productivity and employment uncovers a large drop in labor productivity,

of about two thirds of the decline in output at the trough, which is also highly persistent.

As the third panel shows, financial crises also involve persistent declines in employment.

Finally, Figure 5 displays time series on TFP and patent and trademark applications by

residents in South Korea. As shown in the top left panel, the 1997 financial crisis involved a

persistent slowdown in TFP relative to trend. From the bottom left panel, after a moderate

slowdown prior to the crisis, in 1997 TFP plunges by about 6% relative to trend. Consistent

with the evidence just presented, this decline is never recovered. The right top and bottom

panels show patent and trademark applications in Korea. After rising for almost two decades

practically without interruption, both indicators suffered large declines during the crisis

episode, of about 25% for patents, and more than 35% in the case of trademarks. Further,

in the case of patents the decline is considerably persistent. This evidence lends support

to the mechanism introduced in this paper, namely that a large external shock such as

the one suffered by South Korea in 1997, and the financial sector problems resulting from

it, may lead to a reduction in the pace at which the economy introduces and adopts new

technologies, which results in a permanent TFP loss. Such effects of finance on technology

are consistent with results found by other authors such as Kortum and Lerner (2000) and

Kerr and Nanda (2009), for the case of the US.5 The hypothesis that difficult access to

external finance hinders technology innovation and adoption activity is also supported by

4See appendix A for a list of the countries used in the analysis and details on the data.5Kortum and Lerner (2000) establish a positive effect on innovation of the availability of venture capital

funding, and Kerr and Nanda (2009) show that US financial reforms enhanced the process of small firmentry.

several firm-level studies – see Hall (2002) and Hall and Lerner (2009) for surveys of work

using data from OECD countries. There is also substantial evidence documenting such effects

for developing economies: see Ayyagari et. al. (2007), and particularly Gorodnichenko and

Schnitzer (2010), for studies using firm-level survey data from developing economies.

The evidence described above confirms that the large productivity drop associated with

financial crises in emerging countries is indeed a general phenomenon across episodes and

countries. The magnitudes uncovered by the exercise are comparable to those found by

other authors, such as Meza and Quintin (2005) or Kehoe and Ruhl (2009). Further, these

productivity drops tend to have a very large permanent component in emerging markets,

lending support to the hypothesis put forward by Aguiar and Gopinath (2007) that in these

countries “the cycle is the trend”. There is also some evidence suggesting that the behavior

of TFP can be related to technological factors. In the following sections I introduce a

quantitative model that is capable of generating drops in TFP and productivity of size and

persistence comparable to those in the data, thereby accounting for slow recoveries following

financial crises, and I show that frictions in the financing of the adoption of new innovations

contribute to a substantial degree in accounting for these drops.

3 The Model

The core framework is a small open economy model with endogenous TFP growth through

an expanding variety of intermediates, as in Romer (1990) and Comin and Gertler (2006).

The difference with respect to these frameworks is that there is an imperfection in financial

markets in the form of costly enforcement that impedes the smooth flow of resources from

savers (households and international investors) to entrepreneurs, who are the agents with

the ability to introduce new intermediates. I introduce three further modifications that

have become common in the DSGE literature recently, and that help the model produce

a more realistic behavior of macroeconomic aggregates in response to the crisis: variable

capital utilization, habit formation in consumption, and a working capital requirement on

intermediate goods producers.

As in familiar “financial accelerator” models, frictional credit markets generates an am-

plification effect, inducing a greater slowdown in adoption activity relative to a benchmark

without financial frictions. The rise in country interest rates, and the consequent fall in

the value of the assets controlled by entrepreneurs (adopted and unadopted technologies)

worsen the agency problem between entrepreneurs and lenders and reduce the flow of credit

to entrepreneurs, implying a decline in new technology investments relative to the frictionless

benchmark.

There are six types of agents in the model: households, entrepreneurs, innovators, cap-

ital producers, intermediate goods producers and final goods producers. Final output is

produced by the latter using an expanding variety of intermediates. The entrepreneurial

sector purchases innovations, interpretable as “unadopted” technologies, using funds bor-

rowed from abroad and from domestic households. If successfully adopted, an innovation

becomes a new variety of intermediate. In what follows, I discuss the behavior of each of

these agents in turn, and derive the aggregate relationships that characterize the balanced

growth path of the model economy.

3.1 Households

Suppose there is a representative family with a unit measure of members. Households make

decisions on consumption, labor supply, investment in physical capital and saving through a

risk-free international bond. There are two types of members within each household: workers

and entrepreneurs, with measures f and (1− f) respectively. A fraction of the workers are

specialized or “skilled” workers, and supply labor inelastically to the innovation sector. Their

role will be clear as I discuss innovators below. Regular workers supply labor elastically to

intermediates producers. Both types of labor return wages to the family. Entrepreneurs

have the ability of adopting new types of intermediates, and also transfer any earnings

from this activity back to the household. The following subsection describes the activity of

entrepreneurs in detail. There is perfect consumption insurance among family members. As

in Gertler and Kiyotaki (2010), this formulation is a simple way of introducing heterogeneity

in terms of borrowers and lenders while maintaining the tractability of a representative agent

model.

There is random turnover between entrepreneurs and workers: an entrepreneur becomes

a worker with probability (1 − σ). At the end of their careers, entrepreneurs transfer to

the family the value of the assets they have accumulated. At the same time, each period a

fraction (1−σ) f1−f of workers start a career as entrepreneurs, exactly offsetting the number of

entrepreneurs who exit. As explained below, it is assumed that the family transfers a small

amount of resources to entrepreneurs who start out so they are able to start operations.

Entrepreneur exit is introduced as a device to ensure that the financial imperfection will be

relevant: otherwise entrepreneurs might reach a point where internal resources are enough

to finance all desired investments in new technology.

Letting Ct denote consumption and Lt hours of work in the sector producing intermedi-

ates, a households’ utility function is

u(Ct, Ct−1, Lt) =

(Ct − hCt−1 − Γt

L1+εt

)1−ρ − 1

1− ρ(2)

The preference structure follows Uribe and Yue (2006), Neumeyer and Perri (2005) and

much of the emerging market business cycle literature. It abstracts from wealth effects on

labor supply, as in Greenwood, Hercowitz and Huffman (GHH, 1988). The term multiplying

the disutility of work, Γt, depends on the aggregate technological level, At, as follows:

Γt = Aγt Γ1−γt−1 (3)

The term Γt, which at the low frequency grows at the same rate as At, is introduced

to ensure the existence of a balanced growth path with stationary hours. In the calibrated

version of the model, I will set γ to a very small value, so that fluctuations in At have

a negligible impact on the disutility of labor at high and medium frequencies. Under the

interpretation of GHH preferences as a reduced form for an economy with home production

(Benhabib, Rogerson and Wright (1991) ), a small value of γ can be viewed as capturing a

process of “slow diffusion” of the technologies used in the final goods sector into the home

production sector.

The households’ decision problem is to choose stochastic sequences for consumption,

labor supply, purchases of the international bond and purchases of following-period physical

capital to solve the following problem:

max(Ci,Li,DFi ,Ki+1)

Et∞∑i=0

βiu(Ct+i, Lt+i)

subject to

Ct + PK,tKt+1 ≤ RktKt +WtLt +

DFt −DF

t−1 + τ t

Above, PK,t is the price of capital and Rkt is its rental rate, Wt the wage rate and Rt is

the interest rate on the international bond. DFt denotes the family’s choice of foreign debt

and Kt+1 is the choice for physical capital holdings. Finally, τ t denotes net transfers from

firm ownership plus wages earned by skilled workers.

The international interest rate Rt depends on total net foreign indebtedness Bt, equal to

the sum of household and entrepreneurial debt, and on a random shock rt as follows:

Rt = r + ert + ψ[eBt−BYt − 1

As is usual in the small open economy literature, the reason for introducing a dependence

of the cost of borrowing on net foreign indebtedness is to ensure stationary dynamics. I choose

a very small value for ψ so that this feature does not affect the dyamics of the model. A raise

in rt, interpretable as a country interest rate shock, is a simple way to model the sudden

capital outflows that appear to be the trigger of many of the emerging market financial crises

analyzed in the previous section.

The expression for marginal utility of consumption, UC,t is the following:

UC,t = uC,t − βγEt (uC,t+1) (5)

uC,t =

1 + εL1+εt

)−ρ(6)

Define the households’ stochastic discount factor between periods t and t+ i, Λt,t+i as

Λt,t+i ≡βUC,t+iUC,t

Then the household’s decision on bond and capital holdings are characterized by two

conventional Euler equations:

1 = Et (Λt,t+1)Rt (8)

1 = Et(

Λt,t+1

Labor supply is given by

uC,tΓtLεt = UC,tWt (10)

3.2 Entrepreneurs

The activity of entrepreneurs consists in introducing new varieties of intermediate goods.

Specifically, entrepreneurs use borrowed funds to purchase potential designs for new inter-

mediates. These “innovations” are interpretable as potential new technologies that have not

yet been implemented in the economy, and which may be entirely novel or possibly adapta-

tions of technologies already in use in more advanced countries.6 Unadopted innovations sell

at price Jt. The innovations that entrepreneurs purchase are not yet usable for production

however, and entrepreneurs are the only agents with the ability to turn them into designs

6In the latter case, the assumption is that it is still costly to introduce an innovation that is already inuse in a more developed economy. See Mansfield, Schwartz and Wagner (1981) for evidence suggesting that“imitation” costs can indeed be substantial.

for marketable new intermediates, or “adopt” them. The adoption technology is very sim-

ple: any unadopted project that the entrepreneur is holding becomes a usable design with

probability λ each period. Innovations are subject to the risk of (exogenously) becoming

obsolete: 1−ζ represents the probability of obsolescence. Once an entrepreneur is successful

in adopting an innovation, he then sells the newly adopted technology to a monopolist, who

then proceeds to start manufacturing the new good and sell it to final goods producers. The

price at which sucessfully adopted technologies sell is denoted vt. It will be made clear below

how vt is determined.

The agency friction in financial markets takes the form of a limited enforcement problem

between the entrepreneur and his creditors: at the end of the period, after borrowing funds,

an entrepreneur can default on his debt and divert a fraction θ of his resources, with creditors

only being able to recover the remaining part 1− θ. This imposes a limit on how much debt

the entrepreneur is able to take on ex-ante, as lenders recognize that excessive debt will lead

to default.

In what follows I formally describe an entrepreneur’s problem. The objective of the en-

trepreneur is to choose state-contingent sequences of purchases of innovations and borrowing

in capital markets to maximize expected terminal wealth (recall that an entrepreneur exits

each period with iid probability σ, at which time it pays out any accumulated wealth to the

family that it comes from). The entrepreneur’s wealth consists of the revenues obtained from

selling successful adoptions as well as unadopted innovations, net of debt. The entrepreneur’s

choice is subject to a budget constraint and a no-default constraint, where the no-default

constraint forces the entrepreneur’s continuation value to be greater than the default payoff

– creditors realize that if this were not the case, the entrepreneur would default on his debt.

The formal statement of the entrepreneur’s sequence problem is the following:

maxst+i−1,dt+i−1∞i=1

∞∑i=1

σi−1(1− σ)Λt,t+i [λvt+i + (1− λ)ζJt+i] st+i−1 −Rt+i−1dt+i−1

subject to

Jtst +Rt−1dt−1 ≤ [λvt + (1− λ)ζJt] st−1 + dt (12)

Et∞∑i=1

σi−1(1− σ)Λt,t+i [λvt+i + (1− λ)ζJt+i] st+i−1 −Rt+i−1dt+i−1 ≥ θJtst (13)

From the budget constraint, equation (12), the entrepreneur finances the purchase of

a measure st of innovations, which costs Jtst, and debt repayments, Rt−1dt−1, with the

revenues obtained from previous innovation attempts as well as with new debt issues. From

the innovations that the entrepreneur attempted adopting the previous period, st−1, fraction

λ are successfully adopted during period t − 1, and fraction 1 − λ remain unadopted. The

innovations that are adopted can be sold to monopolists at price vt, while those that remain

unadopted can be sold in the market for unadopted innovations at price Jt, provided that

they survive obsolescence. As indicated by equation (11), if an entrepreneur alive at t exits in

period t+ i (which happens with probability σi−1(1−σ) ) he or she returns the accumulated

wealth back to the household. Thus, an entrepreneur values payoffs in the period and state

at which he exits with the household’s stochastic discount factor, Λt,t+i.

Equation (13) is the entrepreneur’s incentive constraint. At the end of period t, after

having borrowed in capital markets, the entrepreneur may choose to default on his creditors

and divert fraction θ of available funds, which he then transfers back to the household of

which he is a member. Creditors can then force the entrepreneur into bankruptcy and recover

the remaining fraction 1− θ of resources, but it is too costly for them to recover the fraction

θ of funds that the entrepreneur diverted. Accordingly, for creditors to be willing to supply

funds to the entrepreneur, equation (13) must hold: the entrepreneur’s value if he honors

his contract with his creditors must be greater than the value of diverting resources in the

amount θJtst and being shut down.

To simplify the entrepreneur’s problem, define first the rate of return to one dollar in-

vested in technology adoption, RZ,t:

RZ,t ≡λvt + (1− λ)ζJt

Jt−1

RZ,t depends only on the aggregate state, through prices vt and Jt. Times of low re-

alizations of the values of adopted and unadopted technologies, vt and Jt, will be times of

low returns RZ,t. Noting that an entrepreneur’s individual state variables at the beginning

of period t are st−1 and dt−1, the entrepreneur’s problem can be expresssed recursively as

follows:

Vt(st−1, dt−1) = maxst,dt

(1− σ)Et [Λt,t+1 (RZ,t+1Jtst −Rtdt)] + σEt [Λt,t+1Vt+1(st, dt)] (14)

subject to

Jtst +Rt−1dt−1 ≤ RZ,tJt−1st−1 + dt (15)

(1− σ)Et [Λt,t+1 (RZ,t+1Jtst −Rtdt)] + σEt [Λt,t+1Vt+1(st, dt)] ≥ θJtst (16)

Above, the time index on the value function reflects aggregate uncertainty. The problem

can be simplified further by realizing that the key individual state variable will be the

entrepreneur’s net worth wt, defined as the value of his assets (his purchases of innovations)

minus his debt:

wt ≡ Jtst − dt (17)

As shown below, net worth is the key individual state variable because it will determine

the incentives for entrepreneurs to default. From the budget constraint (15) at equality, the

evolution of net worth is

wt = (RZ,t −Rt−1)Jt−1st−1 +Rt−1wt−1 (18)

Net worth at t is given by the gross return to technology adoption activity financed during

t − 1, net of repayments to creditors. Equation (18) shows that net worth at t depends on

the individual state at t− 1 (st−1, wt−1) together with the realization of the aggregate state

at t, through the rate of return RZ,t. This suggests making the following guess for the

entrepreneur’s value function:

Vt(st−1, dt−1) = Ωtwt (19)

where the undetermined coefficient Ωt is conjectured to depend only on the aggregate

state. Define also the following variables:

Ωt+1 ≡ 1− σ + σΩt+1 (20)

µt ≡ Et [Λt,t+1Ωt+1 (RZ,t+1 −Rt)] (21)

νt ≡ Et (Λt,t+1Ωt+1)Rt (22)

Variable Ωt+1 is interpretable as the prospective value of a unit of net worth, before the

entrepreneur finds out whether he will have to exit at the end of the period or not. From

equation (21), µt is interpretable to the return for the entrepreneur of investing in technology

adoption in excess of the cost of funds. Finally, νt represents the value of an extra unit of

net worth today.

With these definitions, the problem of the entrepreneur reduces to the following:

Ωtwt = maxst

µtJtst + νtwt (23)

subject to

µtJtst + νtwt ≥ θJtst (24)

Note that, as discussed above, µt represents the value to the entrepreneur of funding

an additional project (increasing st) while holding net worth constant. On the other hand,

νt is the value of an additional unit of net worth, holding constant st. With frictionless

financial markets entrepreneurs would be unconstrained, with the implication that µt = 0.

The agency problem introduces a friction that makes entrepreneurs potentially constrained

in their activity of financing technology adoption projects, which may place limits on this

arbitrage.

Equation (24) is the incentive constraint. Note that as long as µt ≥ 0, it is profitable

for the entrepreneur to borrow and fund an additional project. Thus, in this instance, and

given wt > 0, the constraint binds:

Jtst =νt

θ − µtwt (25)

Equation (25) shows that the amount the entrepreneur can spend on funding projects,

Jtst, is constrained by his net worth wt, through a limit on the amount the entrepreneur is

allowed to borrow in capital markets.7

Define the entrepreneur’s maximum leverage ratio φt as

φt ≡νt

θ − µt(26)

7Note that for the constraint to bind we must also have µt < θ: otherwise, the value to the entrepreneurof an extra project is greater than the gain from diverting funds, so the incentive constraint does not bind.In the equilibrium constructed below, for reasonable parameterizations the constraint will always be bindingalong the balanced growth path.

so that when the credit constraint binds,

Jtst = φtwt (27)

Then with a binding constraint, solving the undetermined coefficient from (23)-(24) we

have that

Ωt = µtφt + νt (28)

The value of a unit of net worth today (Ωt) derives from its value holding assets constant

(νt) plus the capacity that it generates to fund additional projects (φt) multiplied by the

value to the entrepreneur of those additional projects (µt).

Aggregation. Linearity of (27) makes aggregation simple: the aggregate amount of

projects financed by entrepreneurs, St, is constrained by aggregate net worth of the en-

trepreneurial sector:

JtSt = φtWt (29)

At the same time, aggregate net worth at t is given by the sum of net worth of surviving

entrepreneurs, which evolves individually according to (18), and the transfer that newborn

entrepreneurs obtain from their family. For simplicity I assume that the transfer is a small

fraction ξ of the total value of the projects funded the previous period. Accordingly, the law

of motion of aggregate net worth is given by

Wt = σ [(RZ,t −Rt−1) +Rt−1Wt−1] Jt−1St−1 + (1− σ)ξJt−1St−1 (30)

Note that an important source of fluctuations in aggregate net worth of the entrepreneurial

sector are variations in returns RZ,t, which as discussed above arise from movements in the

prices of adopted and unadopted technologies, vt and Jt.

In what follows I describe the evolution of the aggregate stock of adopted and unadopted

technologies. At the beginning of period t, a total number of innovations Zt exist in the

economy. Each point in [0, Zt] represents a potential new technology. The points between 0

and At correspond to already adopted technologies, with At < Zt. In period t, the innovation

sector (described in the following subsection) introduces a measure ZN,t of new potential

technologies. At the same time, a fraction 1 − ζ of total technologies becomes obsolete.

Thus, the aggregate number of innovations Zt evolves as follows:

Zt+1 = ζZt + ZN,t (31)

Therefore, in period t the points between At and ζZt + ZN,t correspond to technologies

“in process”, i.e. projects that the entrepreneurial sector is currently attempting to adopt.

A fraction λ of these projects will become adopted during period t. The total number of

adopted technologies then evolves as follows:

At+1 = λ [ζZt + ZN,t − At] + ζAt (32)

where the term in brackets is the stock of products that have not yet been converted.

Recall that St refers to the aggregate number of potential technologies that the en-

trepreneurial sector purchases and attempts to adopt. It follows that in equilibrium, we

must have

St = ζZt + ZN,t − At (33)

That is, the total number of projects that entrepreneurs are currently holding and trying

to develop, must be equal to the total number of unadopted projects in the economy.

These considerations clarify how financial factors may affect the evolution of TFP. When

net worth is low, through equation (29) the aggregate number of unadopted projects that

the entrepreneurial sector is attempting to adopt, St, is reduced. This makes demand for

new innovations ZN,t lower, as equation (33) suggests. With a smaller number of products

being attempted to adopt, the growth rate of TFP will decline, as equation (32) indicates.

The Frictionless Benchmark. As emphasized above, with frictionless markets there

is perfect arbitrage, so that excess returns µt must be equal to zero. It follows from (20)-(22)

and (28) that Et(Λt,t+1RZ,t+1) = Et(Λt,t+1)Rt = 1, or

Jt = Et Λt,t+1 [λvt+1 + (1− λ)ζJt+1] (34)

Comin and Gertler (2006) derive a similar equation for optimal adoption. With financial

frictions and constrained adoption, we will have

Jt < Et Λt,t+1 [λvt+1 + (1− λ)ζJt+1] (35)

The gap between the left and right hand side of (35) widens whenever entrepreneurs’

financial constraints tighten, and at the same time the rate of technology adoption falls below

its frictionless level. The imperfection in financial markets also implies that the growth rate

of TFP, and therefore of output, along the balanced growth path will be below its value in

a model without financial frictions.8

3.3 Innovators

The innovations that entrepreneurs purchase and attempt to turn into designs for usable

intermediates are produced in a competitive sector that uses final output and skilled labor,

interpretable as scientists or engineers, as inputs. Specifically, this sector has access to the

following production function:

ZN,t = Nηt (AtLS,t)

1−η (36)

(36) indicates that an innovator using Nt units of final output and LS,t units of skilled

labor used can produce ZN,t new innovations.9 As described in the previous subsection, the

new innovations introduced at time t add to the total stock of potential technologies already

existing. Innovations sell at price Jt. Note that, as in Romer (1990), (36) incorporates

an externality of the aggregate technological level, At, on the efficiency of skilled labor in

introducing new innovations. As Romer (1990) shows, this assumption is key to generate

endogenous growth.

For simplicity, I assume that the aggregate supply of skilled labor is inelastic and fixed

at LS. This assumption, together with perfect competition in producing innovations, can be

shown to generate a positively sloped supply curve of new innovations, given by:

) 1−ηη(ZN,tAt

) 1−ηη

The amount of final output used by the innovation sector is given by:

Nt = ηZN,tJt

3.4 Final Output and Intermediates Producers

The final good is produced in a competitive sector which aggregates a continuum of measure

At of intermediates:

8See Levine (1997, 2005) for surveys of evidence suggesting that financial development has a positiveimpact on long-run TFP and output growth.

9This formulation is common in models of technology innovation and adoption - see for example Santacreu(2010) and references therein. In particular, it captures the spirit of the Nelson-Phelps hypothesis that thestock of skilled labor affects the rate of arrival of potential technologies - see Nelson and Phelps (1966) andBenhabib and Spiegel (1994).

[∫ At

Yt(s)ϑ−1ϑ ds

] ϑϑ−1

Given the aggregator above, demand for each intermediate s is

Yt(s) =

[Pt(s)

]−ϑYt (38)

where the price level Pt is defined as

[∫ At

Pt(s)1−ϑds

] 11−ϑ

Equation (38) gives the demand facing each intermediate good producer s. Intermediates

are produced using a standard Cobb-Douglas technology with capital services ut(s)Kt(s) and

labor Lt(s) as inputs:

Yt(s) = [ut(s)Kt(s)]α Lt(s)

1−α (40)

Intermediate goods firms face a working capital requirement which forces them to hold an

amount of non-interest-bearing assets that is no smaller than a multiple θW of the quarterly

wage bill:

κt(s) ≥ θWWtLt(s) θW ≥ 0

where κt(s) denotes the amount of working capital held by firm s in period t. As shown

in Uribe and Yue (2006) and Mendoza and Yue (2011), this formulation implies that the

effective cost of labor becomes[1 + θW

(Rt−1Rt

)]Wt, and therefore an increase in the interest

rate reduces the demand of labor by intermediates firms.

The objective of intermediates producers is to maximize profits, including the value of

the remaining part of capital they rent from households. Firms face a replacement price of

depreciated capital equal to unity.10 Thus, their objective is to solve

maxPt(s), Yt(s),

ut(s),Kt(s),

Pt(s)Yt(s) + PK,tKt(s)− δ(ut(s))Kt(s)−[1 + θW

(Rt − 1

)]WtLt(s)−Rk

tKt(s)

10As made clear below, adjustment costs are on net rather than gross investment, so that replacingworn-out capital does not involve adjustment costs. This formulation makes the capital utilization decisionindependent of the price of capital.

Subject to (38) and (40). Solving the firm’s problem yields the following equations:[1 + θW

(Rt − 1

)]Wt = (1− α)

Rkt = α

+ PK,t − δ(ut) (42)

αYtut

= δ′(ut)Kt (43)

Per period profits πt can be shown to be equal to

πt =1

It then follows that the price of an adopted technology, vt, corresponds to the expected

present value of profits received by the monopolists from marketing the specialized interme-

diate good:

vt = Et

[∞∑i=0

ζ iΛt,t+iπt+i

Above, (45) incorporates the effect of obsolescence, through parameter ζ. Finally, com-

bining the aggregator (37) with the equations for intermediates producers one obtains an

expression for final output:

Yt = A1

ϑ−1

t (utKt)αL1−α

t (46)

3.5 Capital Producers

At the end of period t, capital producing firms repair depreciated capital and produce new

capital. As in and Gertler et. al. (2007), repair of old capital is not subject to adjustment

costs, but there are stock adjustment costs associated with the production of new capital.

Let Int be net investment, the amount of investment used for construction of new capital

goods:

Int = It − δ(ut)Kt (47)

To produce new capital, capital producers combine final output with existing capital via

the constant returns to scale technology Φ(Int /Kt)Kt, where Φ(·) is increasing and concave

and satisfies Φ(In/K) = 0 and Φ′(In/K) = 1, where In/K is the net investment to capital

ratio along the balanced growth path.

The economy-wide capital stock evolves according to11

Kt+1 = Kt + Φ

(IntKt

)Kt (48)

As in Gertler et. al. (2007), I assume that capital producing firms make production plans

one period in advance, with the objective of capturing the delayed response of investment

observed in the data. Accordingly, the optimality condition for capital producers is

Et−1(PK,t) = Et−1

[Φ′(IntKt

)]−1(49)

3.6 Market Clearing

The economy uses output and international borrowing to finance consumption, investment in

physical capital, and investment in new technology. The resulting market clearing condition

Bt −Bt−1 + Yt = Ct + It +Nt (50)

Bt is economywide foreign indebtedness, equal to the sum of aggregate family and en-

trepreneurial debt (Bt = DFt +Dt). Equation (50) can be derived by combining family and

entrepreneur budget constraints with equilibrium conditions.

The description of the model is now complete.

4 Model Analysis

In this section I present some numerical experiments from a calibrated version of the model.

The goal is to illustrate how the novel mechanism introduced in the paper, namelly finan-

cially constrained technology adoption, may lead to the persistent declines in productivity,

employment and output following financial crises that we observe in the data. The first set

of results concerns the response of the model economy to a “crisis” experiment. The aim is

to illustrate how a sudden stop in capital inflows may lead to a medium run productivity

decline as observed in the data, and how the financial market imperfection may work to am-

plify the decline. It is also shown how employment and output may suffer persistent drops

as a consequence.

11Given the assumptions on Φ(·), to a first order the evolution of capital along the balanced growth pathis the usual Kt+1 = [1− δ(ut)]Kt + It.

I next examine the consequences of a reduction in the “efficiency” of financial markets,

captured in the model by a reduction in the amount lenders are able to recover from en-

trepreneurs in the event of a default, occurring simultaneously with the country interest rate

shock. The aim is to capture a situation like the one in East Asia 1996-97, in which domestic

financial market disruptions accompanied the outflow of capital.

Finally, I also examine the response of the model to two types of non-financial shocks.

In particular, I analyze the effects of exogenous TFP shocks and wage markup shocks.

4.1 Parameter Values

There are a total of nineteen parameters in the model, of which twelve are standard in

the emerging markets business cycles literature. Of the remaining seven, four relate to the

endogenous growth process: the adoption probability (λ), the rate of obsolescence (1 − ζ),

the share of materials used in the innovation sector (η) and the supply of skilled labor (LS).

The remaining three parameters relate to the financial market imperfection. They include

the survival rate of entrepreneurs (σ), the divertable fraction of assets (θ), and the transfer

rate to new entrepreneurs (ξ).

I choose relatively conventional values for the standard parameters. The discount factor

is set at 0.99, and risk aversion is set at unity. I set the inverse Frisch elasticity of labor

supply, ε, equal to one. I set the habits parameter h at 0.2, similar to the value estimated by

Uribe and Yue (2006). The parameter γ governing the impact of the aggregate technological

level At on the labor disutility term Γt is set at 0.01, implying that aggregate technology

impacts the disutility of work only over the very long run. Turning to technology parameters,

I set the capital share α to 1/3, and the quarterly depreciation rate of physical capital, δ,

to 2.5%. Capital utilization along the balanced growth path is normalized to 1, and the

elasticity of marginal depreciation with respect to the utilization rate (δ′′/δ′), is set at 0.15,

as in Jaimovich and Rebelo (2009) and Comin, Gertler and Santacreu (2009). I set the

elasticity of the price of capital with respect to the investment-capital ratio at 0.25, as

in Gertler et. al. (2007) and Bernanke et. al. (1999). I choose the parameter on the

intermediate goods aggregator, ϑ, so that output is proportional to TFP along the balanced

growth path, which by looking at equation (46) amounts to imposing (1 − α)(ϑ − 1) = 1.

This restriction makes profits per period, πt, a stationary variable, and simplifies somewhat

the characterization of the balanced growth path. Given α = 1/3, the resulting value for the

markup is ϑ/(ϑ− 1) = 1.66, close to the value of 1.6 chosen by Comin and Gertler (2006).

Regarding the working capital constraint, I set θW = 0.25, implying that firms need to

pay less than a month’s worth of the wage bill in advance.12 The debt to GDP ratio along

the balanced growth path is set at 0.2, and the elasticity of the interest rate with respect to

the debt-output ratio equals 0.0001 – the latter ensures that the dynamics of the model are

virtually unaffected by the debt-elastic interest rate at high and medium frequencies, while

still making the foreign asset position revert to trend over the long run.

Turning to the parameters governing the TFP growth process, I choose the supply of

skilled labor, LS, to generate an annual TFP growth of 3.0%, similar to the average in

East Asia post-1980. I set the adoption probability λ to obtain an average diffusion lag of

3 years, a value in the high end of the estimates in Pakes and Schankerman (1984). Also

following Pakes and Schankerman (1984) I set ζ to deliver an annual obsolescence rate of 10%.

Finally, based on the presumption that technology production is relatively labor-intensive, I

set η = 0.125, which implies that along the balanced growth path 10% of output is used by

the innovation sector.

The choice of the financial sector parameters is meant to be suggestive. I set the en-

trepreneur survival rate σ = 0.98, implying an expected horizon of entrepreneurs of about

12 years. To calibrate the fraction of resources that entrepreneurs can divert, θ, and the

transfer to new entrants, ξ, I target two features of the balanced growth path of the model

economy: a leverage ratio (assets to equity) of four, and an excess return E(RZ)− R equal

to one hundred basis points annually. The target for the leverage ratio is guided by the

evidence on debt to equity ratios for South Korean chaebols and manufacturing firms prior

to the 1997 crisis, as reported by Krueger and Yoo (2001). These authors document that

these firms were highly leveraged in 1997: the debt-equity ratio was 5.2 for the thirty largest

chaebols, 4.8 for the five largest chaebols, 4.6 for the five largest manufacturing firms and

3.9 for all firms in the manufacturing sector. Thus, an assets-equity ratio of four is relatively

conservative. On the other hand, average debt-equity ratios in the period 1985-1998 are

somewhat lower – around 3.5 for the five largest manufacturing firms, and about 3 for all

manufacturing firms, similar to my chosen value. On the other hand, Gertler et. al. (2007)

document that spreads between corporate and government bonds in Korea appeared to be

consistently zero prior to 1997, which they interpret as evidence of government guarantees

to the Korean corporate sector. For this reason, I instead target an annual spread of a

percentage point, following evidence on spreads between corporate and government bonds

in the U.S. . These targets imply setting the divertable fraction θ at 0.45, and the transfer

rate ξ at 0.01.

12While higher values of this parameter are frequently used in the literature, Mendoza and Yue (2011)argue that it is desirable to set this parameter at a relatively low value, since empirical estimates suggestthat working capital is a small fraction of GDP. A working capital requirement of 0.25, together with a wagebill of two thirds of GDP, implies a ratio of working capital to GDP of around 16%.

Table 1 reports the values chosen for the model parameters together with a reminder of

their meaning.

4.2 Crisis Experiment (1): Interest Rate Shock

In this subsection, I analyze the effects of an unanticipated increase in the country interest

rate. In particular, I consider a 750 basis point increase in rt that persists as a first-order

autoregressive process with a 0.88 coefficient. These magnitudes are close to the evidence for

the crisis in South Korea in 1997, as shown by Gertler et. al. (2007). More generally, large

country interest rate fluctuations are thought to be an important driver of emerging markets

business cycles – see for example Neumeyer and Perri (2005) or Uribe and Yue (2006).

Figure 5 documents the effect of the interest rate shock on the financial side of the

model. The disturbance induces a large decline in the prices of adopted and unadopted

technologies, as the stream of future profits per adopted intermediate good is discounted

more heavily. This has the effect of generating a large drop in aggregate entrepreneurial net

worth, as equation (30) indicates. Notice that the value of unadopted technologies, Jt, falls

substantially more than in the frictionless benchmark: as entrepreneurs’ constraints tighten

(as reflected in the increase in the multipler on the incentive constraint), they are forced

to cut back on project funding to a larger extent than what would happen with frictionless

financial markets. Along the way, there is “adverse feedback” between net worth and the

franchise value Jt: as the former falls, entrepreneurs’ constraints tighten, forcing a decline in

the credit available for projects in development. The decrease in demand for new projects

leads to further reductions in their franchise value Jt.

The tightening of financial constraints is also reflected in the rise in excess returns

Et(RZ,t+1) − Rt, which reflects that profitable opportunities of investment in technology

adoption projects go unexploited due to an intensification of financial market frictions. The

rise in the spread represents a widening of the departure from perfect arbitrage, as exem-

plified by equation (35). The flow of credit to entrepreneurs is reduced substantially as a

consequence of the shock, as the first panel in the last row indicates. Finally, the aggregate

amount of new projects, ZN,t, falls substantially more in the model with frictions compared

to the frictionless model, and the drop is considerably more persistent.

The decline in the number of projects funded by the entrepreneurial sector directly trans-

lates into a decline in the rate of new adoptions. As Figure 6 shows, it follows that there is

a substantial slowdown in the growth rate of TFP, leading to a permanent drop in the level

of this variable relative to its unshocked path. Further, the magnitude of the medium-run

decline is substantially larger due to financial factors – on the order of 50 percent larger

relative to the frictionless model. Thus, the financial friction plays a quantitatively signif-

icant role in helping the model generate a realistic behavior of TFP following a crisis, as

illustrated for example in the case of South Korea reviewed earlier, in which TFP remained

persistently depressed relative to trend by about 6%.

Figure 7 summarizes the key results regarding the effect of the interest rate shock, by

plotting the model counterpart of the empirical impulse responses documented in Section 2:

it displays the behavior of output, labor productivity and employment following the shock,

relative to the unshocked path of the economy. In the case of a frictional financial market,

there is a large permanent component to the decline in output, which is substantially larger

than in the frictionless benchmark – about 2 percentage points larger, 50 percent more than

without frictions. Behind the results in Figure 7 is the behavior of technology adoption

following the crisis, and its impact on aggregate TFP. This is the main driving force behind

the behavior of labor productivity displayed in the figure. At the same time, as shown

in the last panel of Figure 7, the permanent decline in productivity leads to a decline in

labor demand by producers of intermediates. As a result, employment also falls persistenty

relative to the unshocked path of the economy, with an important portion of the decline

being due to financial frictions. Thus, the model is also able to account for the evidence

provided in Section 2 that employment remains persistently depressed following financial

crises. The financial friction helps generate a realistic magnitude of the employment drop:

in the data it is about 4 percent after four years, while in the model with and without

financial frictions it is 3 and 2 percent, respectively. Overall, the bottomline from Figure 7

is that the mechanisms introduced in the model appear to have potential for quantitatively

accounting for the behavior of output, labor productivity and employment following financial

crises.

Finally, Figure 8 plots the response of a set of standard macroeconomic variables. Overall,

the model does a relatively good job of capturing quantitatively the macroeconomic effects

of the typical emerging markets financial crisis. In particular, the responses of the variables

displayed in Figure 11 are reasonably close to the evidence for the Korean 1997 crisis, as

documented for example in Gertler et. al. (2007), especially regarding the magnitude of the

decline in investment and the large reversal in the net exports to GDP ratio. As discussed

above, the mechanisms introduced in this paper help in accounting for the persistence in

the output decline following these episodes. A final point to highlight from Figure 11 is the

substantial amplification due to the financial friction of aggregate consumption, a variable

which is well known to display higher volatility relative to GDP in emerging markets when

compared to more developed economies, and also of the ratio of net exports to GDP.

4.3 Crisis Experiment (2): Tightening Margins

In the preceding subsection, a financial crisis was triggered by an unanticipated increase in

the country interest rate. This was meant to capture the sudden outflow of capital that

has often afflicted emerging market economies in recent times. A complementary way in

which financial distress can transmit to the real economy is by a tightening of entrepreneurs’

leverage ratio, arising from an intensification of agency problems in financial markets. In

particular, suppose that the fraction of assets that lenders can recover, θ, might vary. An

increase in θt is interpretable as a reduction in the efficiency of financial markets, as lenders

are able to recover a smaller amount from defaulting borrowers.13

With a time-varying θt, equation (29) now becomes

JtSt =νt

θt − µtWt (51)

Clearly, an increase in θt will reduce the aggregate amount of projects funded by en-

trepreneurs: as the incentive constraint tightens, lenders are willing to extend less credit per

unit of net worth.

Figure 9 illustrates the implications of an increase in θt occurring simultaneously with the

interest rate shock. Specifically, θt rises to 0.75 from its steady state value of 0.45, and the

increase persists as a first order autoregressive process with coefficient 0.95. As a result, the

slowdown in the rate of introduction of new products is substantially more severe. It follows

that the magnitude of the medium-run decline in productivity, employment and output is

considerably greater, and closer to the empirical magnitudes reported in Section 2.

4.4 Non-financial Shocks

In this subsection, I analyze the behavior of the model economy following two types of non-

financial shocks that have been highlighted in the literature as important sources of business

cycle fluctuations: an exogenous TFP shock, and a wage markup shock. To introduce the

former, I modify the production function of intermediate goods firms as follows:

Yt(s) = At [ut(s)Kt(s)]α Lt(s)

1−α (52)

Above, At is an exogenous aggregate TFP shock. To introduce the wage markup shock,

the labor supply equation is modified according to the following:

13Kiyotaki and Moore (2008), Del Negro, Eggertsson, Ferrero and Kiyotaki (2010) and Jermann andQuadrini (2009) use a mechanism in this spirit to motivate a disruption in financial markets.

Wt = µWtuC,tΓtL

UC,t(53)

µWt is a markup of the wage over the household’s marginal disutility of work. Several

authors have argued that countercyclical movements in the wage markup are an important

source of business fluctuations,14 possibly by capturing in a reduced-form way the effects of

nominal price and wage rigidities or labor market frictions.

Figures 10 and 11 report the effects of a 5% decline in exogenous TFP and a 5% increase

in the wage markup, respectively. Both shocks persist as an AR(1) with a 0.95 coefficient.

The key point to note is that both shocks induce only modest declines in the endogenous

component of TFP, and that the degree of amplification through the credit market imper-

fection is also relatively small. The reason is that unlike financial shocks, these two types

of shocks induce modest movements in the prices of adopted and unadopted technologies,

vt and Jt. As a consequence, their adverse impact on the financial constraints of technology

adopters is relatively small. As the figures show, it follows that these types of disturbances

are followed by a recovery, which is driven by the unwinding of the shock. Thus, the bot-

tomline from Figures 10 and 11 is that the model is also consistent with the evidence that

slow recoveries are a phenomenon especially associated with financial crises, as Reinhart and

Rogoff (2009) and others have noted.

5 Concluding Remarks

This paper has sought to explain the phenomenon of slow recoveries following financial crises.

It has argued that the large and persistent productivity and TFP declines observed during

banking crises in emerging economies can be a natural consequence of an adverse shock in

an environment in which productivity growth is endogenous through the adoption of new

technologies. Further, it has shown how domestic financial market disruptions can work to

amplify these declines. The model is able to deliver the persistent declines in output, labor

productivity and employment following financial crises in a manner that is quantitatively

consistent with the evidence. The model is also shown to generate reasonable behavior of

macroeconomic aggregates, with the financial friction delivering substantial amplification of

consumption and the current account. Finally, the model predicts that the lack of recovery

is more severe following financial shocks than following nonfinancial shocks, also consistent

with what we observe in the data.

While the evidence motivating the model introduced in this paper has been based on

14See Hall (1997), Galı, Gertler and Lopez-Salido (2007) and Chari, Kehoe and McGrattan (2007).

the experience of emerging market economies – after all, it is in these countries that most

financial crises have occurred over the past decades – the recent experience in the U.S. and

Europe in the aftermath of the Great Recession suggests that the mechanism identified in

this paper may be relevant to industrialized countries as well.

A potentially interesting application of the framework presented in this paper would be

an evaluation of the welfare gains of government intervention in mitigating a financial crisis.

Gertler and Karadi (2009) and Gertler, Kiyotaki and Queralto (2011), for example, analyze

different government financial policies in the context of the recent financial crisis in the US,

finding important benefits of government intervention. The endogenous productivity growth

mechanism introduced in this paper would likely affect what is at stake when considering

intervention during a financial meltown, and therefore it could have a substantial impact on

the welfare gains of government policies directed at ameliorating the impact of a financial

crisis.

6 Appendix

A Data

Financial crises. Banking crisis dates are obtained from Caprio and Klingebiel (2003). I

obtain output and employment data from the Total Economy Database15, maintained by

the Conference Board and the Groningen Growth and Development Centre, which contains

yearly series for 90 countries for the period 1950-2009. The list of emerging countries used in

the analysis is the following: Argentina, Brazil, Chile, China, Colombia, Hong Kong, Hun-

gary, India, Indonesia, South Korea, Malaysia, Mexico, Peru, Philippines, Poland, Singapore,

Thailand, Turkey and Vietnam.

B The Complete Model

B.1 Conventional Part

Production function:

Yt = A1

ϑ−1

t (utKt)αL1−α

t (54)

Marginal utility of consumption:

UC,t = uC,t − βhEt (uC,t+1) (55)

uC,t =

1 + εL1+εt

)−ρ(56)

Labor market equilibrium:

uC,tΓtLεt

1 + θW

(Rt−1Rt

)(1− α)YtLt

Stochastic discount factor:

Λt,t+1 =βUC,t+1

UC,t(58)

International bond Euler Equation:

15http://www.conference-board.org/economics/database.cfm

1 = Et (Λt,t+1)Rt (59)

Capital Euler Equation (demand for capital):

1 = βEt

(Λt,t+1

α Yt+1

Kt+1+ PK,t+1 − δ(ut+1)

Supply of capital:

Et−1(PK,t) = Et−1

[Φ′(IntKt

)]−1(61)

Net investment:

Int = It − δ(ut)Kt (62)

Capital accumulation:

Kt+1 = Kt + Φ

(IntKt

)Kt (63)

Optimal utilization:

αYtut

= δ′(ut)Kt (64)

Market clearing:

Bt −Bt−1 + Yt = Ct + It +Nt (65)

International bond price:

Rt = r + ert + ψ[eBt−BYt − 1

B.2 Endogenous Growth and Financial Frictions Part

Profits per intermediate good:

πt =1

Value of a new intermediate good:

vt = πt + ζEt(Λt,t+1vt+1) (68)

Evolution of aggregate net worth:

Wt = σ [(RZ,t −Rt−1) +Rt−1Wt−1] Jt−1St−1 + (1− σ)ξJt−1St−1 (69)

Constraint on technology adoption:

Jt [ζZt + ZN,t − At] = φtWt (70)

Value function coefficients:

Ωt+1 = 1− σ + σ (νt + φtµt) (71)

µt = Et [Λt,t+1Ωt+1 (RZ,t+1 −Rt)] (72)

νt = Et (Λt,t+1Ωt+1)Rt (73)

Evolution of adopted and unadopted technologies:

At+1 = λ [ζZt + ZN,t − At] + ζAt (74)

Zt+1 = ζZt + ZN,t (75)

Price of innovations:

) 1−ηη(ZN,tAt

) 1−ηη

Materials used in innovation sector:

Nt = ηZN,tJt (77)

In the frictionless benchmark, the following equation holds:

Jt = Et Λt,t+1 [λvt+1 + (1− λ)ζJt+1] (78)

The model is solved by first appropiately detrending the variables that exhibit long-run

growth. With the redefined “detrended” variables, a stationary system obtains. The steady

state of that system characterizes the balanced growth path of the economy. Dynamics are

obtained by computing a loglinear approximation around the balanced growth path.

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Table 1: Calibration

Symbol Value Description

Conventionalβ 0.99 Discount factorρ 1 Risk aversionε 1 Inverse Frisch elasticityh 0.20 Habitsγ 0.01 Parameter on labor disutility termδ 0.025 Capital depreciationα 1/3 Capital shareδ′′/δ′ 0.15 Elasticity of depreciation to utilizationϑ 2.5 Demand elasticity for intermediatesΦ′′(In/K) 0.25 Elasticity of Pk to In/KθW 0.25 Working capital requirementψ 0.0001 Elasticity of interest rate to foreign debtB/Y 0.2 Foreign debt to outputGrowthλ 0.08 Probability of adoption1− ζ 0.025 Obsolescence rateη 0.125 Final output share in innov.

LS 0.4725 Skilled labor supplyFinancial Frictionsσ 0.98 Survival rateθ 0.45 Fraction divertableξ 0.01 Transfer rate

1980 1985 1990 1995 2000 2005 201013.5

16Output for SEA−6 (log)

1980 1985 1990 1995 2000 2005 20102

Labor Productivity for SEA−6 (log)

1980 1985 1990 1995 2000 2005 201011.5

12.5Employment for SEA−6 (log)

Figure 1: Total output, employment and output per employed worker (logs) for group of 6 SouthEast Asian countries (Indonesia, Malaysia, Phillipines, Korea, Thailand and HongKong).

1980 1985 1990 1995 2000 2005 20101.8

3.2Labor Productivity for SEA−6 (log)

1992 1994 1996 1998 2000 2002 2004 2006−0.2

−0.1

0.1Labor Productivity for SEA−6 (log, detrended)

Figure 2: Labor productivity (log) for group of 6 South East Asian countries (Indonesia, Malaysia,Phillipines, Korea, Thailand and Hong Kong).

0 2 4 6 8 10−11

−2Output

0 2 4 6 8 10−6

0Employment

0 2 4 6 8 10−7

0Labor Productivity

Figure 3: Estimated impulse responses to a banking crisis. Time measured in years.

1990 1995 2000−0.5

−0.4

−0.3

−0.2

−0.1

0.3 TFP, South Korea (log)

1990 1995 2000

−0.1

−0.08

−0.06

−0.04

−0.02

0.02TFP, South Korea (log, relative to linear trend)

1990 1995 2000

Patent applications by residents, South Korea (log)

1990 1995 200010

11.6Trademark applications by residents, South Korea (log)

Figure 4: TFP, patents and trademarks, South Korea.

0 2 4 6 8 100

0.1R (shock)

0 2 4 6 8 10−0.4

−0.2

0Value adopted, v

0 2 4 6 8 10−1

−0.5

0Value unadopted, J

0 2 4 6 8 10−1

−0.5

0Aggregate net worth, W

0 2 4 6 8 10−0.05

E(RZ) − R

0 2 4 6 8 10−0.1

0.2Multiplier on Incentive Constraint

0 2 4 6 8 10

−0.1

−0.05

0Aggregate entrepreneurial debt, D

0 2 4 6 8 10

−0.1

−0.05

Aggregate New Projects, ZN

Financial Frictions

Frictionless Adoption

Figure 5: Impulse responses to interest rate shock, endogenous growth and financial frictionsvariables. Time measured in years.

0 2 4 6 8 10−5

−3 Growth Rate of TFP

0 2 4 6 8 10−0.04

−0.03

−0.02

−0.01

Financial FrictionsFrictionless Adoption

Figure 6: Impulse responses to interest rate shock, TFP growth rate and TFP. Time measured inyears.

2 4 6 8 10−0.08

−0.07

−0.06

−0.05

−0.04

−0.03

−0.02

−0.01

Output

Years2 4 6 8 10

−0.04

−0.035

−0.03

−0.025

−0.02

−0.015

−0.01

−0.005

0.005Labor Productivity

Years2 4 6 8 10

−0.04

−0.035

−0.03

−0.025

−0.02

−0.015

−0.01

−0.005

0.005Employment

Financial FrictionsFrictionless AdoptionExogenous Growth

Figure 7: Responses of output, labor productivity and employment to interest rate shock.

0 2 4 6 8 100

0.08R (shock)

0 2 4 6 8 10−0.08

−0.06

−0.04

−0.02

0 2 4 6 8 10−0.04

−0.03

−0.02

−0.01

0 2 4 6 8 10

−0.4

−0.3

−0.2

−0.1

0 2 4 6 8 10−0.08

−0.06

−0.04

−0.02

0 2 4 6 8 10

Net Exports / GDP (level)

Financial Frictions

Exogenous Growth

Figure 8: Impulse responses to interest rate shock, macroeconomic variables. Time measured inyears.

0 2 4 6 8 100

0.08R (shock)

0 2 4 6 8 100

0.8Fraction divertable, θ (level)

2 4 6 8 10−0.1

−0.08

−0.06

−0.04

−0.02

Output

Years2 4 6 8 10

−0.05

−0.04

−0.03

−0.02

−0.01

Labor Productivity

Years2 4 6 8 10

−0.05

−0.04

−0.03

−0.02

−0.01

Employment

steady state θ

R shock + Tightening Margins

R shock only

Exogenous Growth

Figure 9: Responses of output, labor productivity and employment, tightening margins togetherwith interest rate shock.

2 4 6 8 10−0.06

−0.04

−0.02

0Exogenous TFP shock

0 2 4 6 8 10−0.4

−0.2

0 2 4 6 8 100

−3 E(RZ) − R

2 4 6 8 10−10

−3 A

2 4 6 8 10−0.2

−0.1

0Output

Years2 4 6 8 10

−0.1

−0.05

0Labor Productivity

Years2 4 6 8 10

−0.1

−0.05

0Employment

Financial Frictions

Exogenous Growth

Figure 10: Responses of net worth, spread, TFP, output, labor productivity and employment toexogenous TFP shock.

2 4 6 8 100

0.06Wage markup shock

0 2 4 6 8 10−0.2

−0.1

0 2 4 6 8 100

−3 E(RZ) − R

2 4 6 8 10−4

−3 A

2 4 6 8 10−0.06

−0.04

−0.02

0Output

Years2 4 6 8 10

−0.01

0.01Labor Productivity

Years2 4 6 8 10

−0.06

−0.04

−0.02

0Employment

Financial Frictions

Exogenous Growth

Figure 11: Responses of net worth, spread, TFP, output, labor productivity and employment towage markup shock.

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